Non-parametric sequential prediction project

Non-parametric sequential prediction project

Abstract
The central theme is to explore which regularities are “learnable” from sequential data. Specifically, this general question is considered for the problems of probability forecasting and bandits and possibly with related statistical problems concerning sequential data. Probability forecasting is concerned predicting the probabilities of future outcomes of a series of events given the past. The question to be addressed is: under which assumptions on the stochastic mechanism generating the data is it possible to give fore- casts whose error becomes negligible as more data becomes available? Here we specifically allow for the possibility that the predictions are based on a model that is ‘wrong yet useful’, i.e. it does not contain the data generating mechanism. In this ’nonrealizable’ or ’misspecified’ case, the question becomes: under what conditions it is possible to give forecasts that converge to the best available ones as more data becomes available ? Questions of this kind find applications in a variety of fields, such as finance, data compression, bioinformatics, environmental sciences, and many others. However, the research topic is mainly about theoretical foundations rather than applications.